Summary

o notation

f(n) = o(g(n)), g(n) is an upper bound of f(n) that is not asymptotically tight

$\omega$ notation

f(n) = $\omega(g(n))$, g(n) is a lower bound of f(n) that is not asymptotically tight

Example: f(n) = 3n³ + 4

• f(n) = $\Theta(n^3)$
• f(n) = O(n³) = O(n⁴) = ...
• f(n) = $\Omega(n^3)$ = $\Omega(n^2)$ = $\Omega(n)$ = $\Omega(1)$
• f(n) = o(n⁴) = o(n⁵) = ...
• f(n) = $\omega(n^2)$ = $\omega(n)$ = $\omega(1)$